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In traditional economic theory, few concepts have as respected a position as that of equilibrium. The concept of equilibrium suggests that the economy transitions smoothly from one state to another, with the supply of goods perfectly balancing out the demand for goods. Such a mechanical clockwork-like operation was implied by the first great economist, Adam Smith (1723-1790), in his magisterial book, The Wealth of Nations. He conjured up the metaphor of the “invisible hand” to describe the economy’s ability to self-regulate.
The problem with this pretty picture as anyone who reads magazines about business and the economy would have noticed, is that the economy and by extension markets have a habit of slipping into instability. They experience booms and busts from time to time. Traditional economists tend to explain this away by saying that the booms and busts are anomalies that are not inherent features of the market and that they come about through causes that are external to the economy (the economic jargon for this is that they are caused by exogenous events). Common examples of these external causes given by economists are the introduction of new technology and the change in government policy/regulations.
Not all economic thinkers agree/agreed with the traditional economists’ assessment of market instability. Arguably, the most influential dissenter was Karl Marx (1818-1883), whose ideas on socialism led roughly one third of the globe to declare themselves communist countries in the 20th century. In an equally magisterial book titled Das Kapital that came in three volumes, Marx countered the position of the traditional economists by suggesting that booms and busts are an intrinsic feature of a capitalist society. His reasoning was that since in a capitalist society, the means of production is in the private hands of autonomous individuals scattered across the economy, capitalist societies suffer from huge coordination problems that result in fluctuations that ultimately bring about the booms and busts. He concluded by saying that these booms and busts would lead to the demise of capitalism and usher in the age of communism, what he referred to as the “proletariat revolution”.
Well, it seems safe to say that Marx was wrong about the demise of capitalism. Capitalism is clearly alive and well (Okay, some might disagree with the well part). Nevertheless, there are those who believe that Marx was onto something when he said that there are natural fluctuations that arise within the economy that give it bouts of instability. Physicists interested in economics had begun to take that line of reasoning shortly after Marx’ death.
One of the most influential works done by physicists about market fluctuations was carried out by Frenchman Louis Bachelier (1870-1946) and was published in a thesis titled Theorie de la Speculation (Theory of Speculation) in the year, 1900. Bachelier’s contention was that the fluctuations in the prices of stocks and shares, and thus the underlying structure of the market economy, are random. To reach this conclusion, he had to formulate what is now known as random walk theory, a theory that went on to have and continues to have a huge impact on the world of finance. In secondary school, you were exposed to random walk theory when you were taught “Brownian motion” in biology. For you to get a sense of how big an achievement random walk theory was, I will point out that the great Albert Einstein himself used random walk theory to explain Brownian motion and thus decisively prove the existence of atoms, which at the time was contestable, 5 years after Bachelier came up with it.
The direction of motion of a particle undergoing a random walk fluctuates unpredictably, and Bachelier assumed that stock prices did the same. If you plotted a graph of the size of the fluctuation of such a particle against the number of times such a similarly sized fluctuation appears, you will get the all too familiar “bell curve”. The bell curve is the mathematical signature of a random process.
Bachelier’s theory was indeed a very brilliant one, but it had one problem. It wasn’t quite correct. Close examination of stock price fluctuations show that they aren’t quite random. What’s more if you model stock price fluctuations as a random walk, the resulting distribution of fluctuations suggest that booms and busts occur much less often than they actually do in real life markets. The danger of this is that financial traders that use random walk models (which is to say just about everybody using statistical trading models) could get hit by a financial market crash that they never saw coming. Sound familiar?
Physicists attempts to model stock price fluctuations did not stop with bell curve distributions (formally known as the normal distribution or Gaussian distribution, so named after 19th century German mathematical genius Friedrich Gauss). In the 1960s, French mathematician Benoit Mandelbrot, who played a crucial role in the development of chaos theory, suggested that stock price variations could be modeled using a Levy flight, named after another French mathematician Paul Levy (1886-1971), who came up with the idea in 1926. Levy flights are similar to random walks except that they from time to time, exhibit some very large fluctuations relative to the size of the vast majority of fluctuations. In a true random walk, all variations are roughly the same size. Processes that can be modeled this way are known as Levy-stable processes.
In modeling stock price variations, the Levy-stable process is a significant improvement over the Gaussian distribution. Financial practitioners, however overwhelmingly still use Gaussian models because they are much easier to handle. Despite the improvement it brings, the Levy-stable process is not perfect. Where the Gaussian distribution severely underestimates large fluctuations, the Levy-stable process overestimates them, but to a significantly less degree than the Gaussian distribution underestimates them. It seems the true curve lies somewhere in between. Further research by physicists and other scientists have not been able to locate a single curve that captures price variations perfectly, but they have found that the behaviors price variations exhibit is consistent across many global financial markets, suggesting that perhaps, capitalism has a universal statistical signature.
The models discussed above try to describe market fluctuations without bothering about their source. Common sense suggests that the source are the interactions of buyers and sellers in financial markets, an observation that could be reasonably extended to the larger economy. However, traditional economics treats each and every market participant as independent, assuming that we never interact with one another. For instance, if someone wanted to buy a car, traditional economics assumes that the person would gather every bit of information there is on the car market, logically analyze all the information and independently come up with the most rational choice of car to buy, without ever asking another human being for his/her opinion or looking to see what other people interested in buying cars are buying. You are probably laughing by now. Well don’t. You probably wouldn’t have done much better if you were an economist. You see, modeling how our interactions affect our economic decisions is a very complex problem, and until recently, economists did not have the tools to model those interactions adequately, so they left them out of their economic models.
This is precisely where physics can help. Statistical physicists have been dealing with systems of interacting particles for over a century. While one would not expect their tools to translate perfectly from physics to economics, some useful insights can be gleaned. The class of models that have been borrowed from physics to model interactions in economics are known as “interacting-agents” models. The first of such models was developed in 1974 by a German mathematician familiar with both physics and economics. Interacting-agents models are based on models from the field of magnetism known as Ising models. Ising models model the interaction of atoms in a magnet. For those of you who did physics in secondary school, you might recall that atoms have a characteristic spin where it could spin in one direction or the other. Each atom’s choice of spin is affected by its neighbors. In the same vein, interacting-agents models present each economic agent with choices of how to trade, with the agent’s choice being affected by other economic agents. One very useful result that has come from the use of interacting-agents models is that the phenomenon of herding, where agents copy one another, emerge naturally from the models, an impossibility with traditional economic models because of the assumption of independent agents. Given how often the phenomenon of herding has been fingered in market crashes, one can hardly argue that interacting-agents models haven’t made a useful contribution to the field of economic modelling.
Bibliography
- Ball, Philip. 2005 Critical Mass: How One Thing Leads to Another. London: Arrow Books
